find your main shutoff for the home
usually on the front wall of house, in basement if you have one, near the water meter
shut off the water main, this is the way you service a tub faucet as there is no provision for just shutting the tub in most homes, like you would find under a sink or toilet. tubs are shut at the main
then go ahead asnd service you fauset washer
i would replace both hot and cold as long as your doing one do both
BTW, your probally going to need a tub wrench, is a deep socket set that are very inexopensive, this enables you to get the stem out
also, flowing water will not freeze, so dont worry about the dripping faucet freezing, its the other lines that will freex
let me know if you need anynmore help or let us know if you indeed fix it!